Warm-Up #76
1/5/17
Solve the following system of equations… 1. Using substitution.
Systems with Three Variables
2. Using elimination.
Section 3-5 Started on 12/9/16 EQ: How can you use the algebraic methods needed to solve a system of two equations to solve a system of three equations?
Solving Systems with Three Variables We can solve a system of equations in three variables using substitution and elimination, like we did for systems of two equations. This solution, written as an ordered triple (x, y, z), is the intersection of the planes.
Steps for solving using substitution: 1. Solve one of the equations for x, y, or z. 2. Substitute this new equation into the other two equations. 3. Write these two new equations as a new system and solve for the two variables. 4. Use these two variables to find the third one using one of the original equations. Best method to use when (0, 1, 7) you can easily solve one of the equations for a single variable.
Section 3-5 Practice: Using Substitution
Warm-Up #77
Solve each system by substitution. Check your answers.
Solve the following system of equations by substitution.
1.
2.
(8, -4, 2)
(4, 1, 6)
1/6/17
Section 3-5 Practice: Using Substitution
Solving a System Using Elimination
Solve each system by substitution. Check your answers.
Elimination is the best method to use when you can easily eliminate (“ get rid of ”) one variable.
1.
2.
(8, -4, 2)
Warm-Up #78
(4, 1, 6)
(3, 3, 1)
1/9/17
Solve the following system of equations by elimination.
1. Pair the equations (1 & 2 and 2 & 3) to eliminate z. 2. Write the two new equations as a system. Solve for x & y. 3. Solve for z. Substitute the values of x and y into one of the original equations.
Steps for using elimination: 1. Pair the equations to eliminate one of the variables (x, y, or z). 2. Write these two new equations as a new system and solve for the two variables. 3. Use these two variables to find the third one using one of the original equations. (4, 2, -3)
Now try...
Solving a Real-World Problem
Section 3-5 Practice: Using Elimination
You manage a clothing store and budget $6,000 to restock 200 shirts. You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for $36 each. If you want to have twice as many rugby shirts as polo shirts, how many of each type of shirt should you buy?
Solve each system by elimination. Check your answers.
20 T-shirts, 60 polo shirts, and 120 rugby shirts
1.
2.
(0, 2, -3)
(-3, 1, -1)
Warm-Up #79 Solve the following system of equations.
1/10/17
Section 3-5 Practice: Using Elimination Solve each system by elimination. Check your answers. 1.
2.
(0, 2, -3)
(-3, 1, -1)
